流体力学北航教学课件电子版第一章

2023/12/71

SchoolofJetPropulsionBeihangUniversity.FLUIDMECHANICS2023/12/72Chapter1Introduction1.1PreliminaryRemarks

Whenyouthinkaboutit,almosteverythingonthisplaneteitherisafluidormoveswithinorneara

fluid.-FrankM.WhiteWhatisafluid?2023/12/73

TheconceptofafluidAsolidcanresistashearstress(剪切应力)byastaticdeformation,afluidcannot.Anyshearstressappliedtoafluid,nomatterhowsmall,willresultinmotionofthatfluid.Thefluidmovesanddeformscontinuouslyaslongastheshearisapplied.2023/12/74WhatisFluidMechanics

FluidMechanicsisthestudyoffluideitherinmotion(FluidDynamics流体动力学)oratrest(FluidStatics流体静力学)andsubsequenteffectsofthefluidupontheboundaries,whichmaybeeithersolidsurfacesorinterfaceswithotherfluids.2023/12/75ThefamouscollapseoftheaNarrowBridgein1940Curvedshoot(Bananashoot)NospinSpinwhy2023/12/76Boeing74770.7×64.4×19.41(m)395000kgAn-22584×88.4×18.1(m)600,000kg

Howcantheairplanefly?Drag&Lift2023/12/772023/12/78Theengineofaturbofan(涡扇)jet2023/12/79；2023/12/710HistoryandScopeof

FluidMechanicsPre-history:Sailingshipswithoars(橹桨)andirrigationsystemwerebothknowninprehistory2023/12/711Archimedes(285-212BC)Parallelogramlawforadditionofvectors

Lawofbuoyancy2023/12/712LeonardodaVinci(1452-1519)*Equationofconservationofmassinone-dimensionalsteadyflow*Experimentalist*Turbulence2023/12/713IsaacNewton(1642-1727)LawsofmotionLawsofviscosityofNewtonianfluid2023/12/714

18thcenturyMathematicians：Euler（欧拉）：

EulerequationBernoulli(伯努利)：BernoulliequationFrictionless(无粘)flowsolutionsD’Alembert（达朗贝尔）：

D’Alembertparadox（佯谬，疑题）Engineers：Hydraulics（水力学）relayingonexperimentChannels，Shipresistance，Pipeflows，WaveturbinePitotVenturiTorricelliPoiseuille2023/12/71519thcenturyNavier(1785-1836)

&

Stokes(1819-1905)N-Sequation

viscousflowsolutionReynolds(1842-1912)

TurbulenceFamousexperimentontransitionReynoldsNumber2023/12/71620thcenturyLudwigPrandtl

(1875-1953)Boundarytheory(1904)Tobethesinglemostimportanttoolinmodernflowanalysis.ThefatherofmodernfluidmechanicsVonkarman(1881-1963)I.taylor(1886-1975)Laidfoundationforthepresentstateoftheartinfluidmechanics2023/12/7171.2TheFluidasaContinuum(连续介质）Density(密度)Elementalvolume（流体微团、流体质点）*Largeenoughinmicroscope（微观）10-9mm3ofairatstandardconditionscontainsapproximately3×107molecules.Sodensityisessentiallyapointfunctionandfluidpropertiescanbethoughtofasvaryingcontinuallyinspace.*Smallenoughinmacroscope（宏观）.Mostengineeringproblemsareconcernedwithphysicaldimensionsmuchlargerthanthislimitingvolume.2023/12/718TheelementalvolumemustbesmallenoughinmacroscopeSuchafluidiscalledacontinuum,whichsimplymeansthatitsvariationinpropertiesissosmooththatthedifferentialcalculuscanbeusedtoanalyzethesubstance.2023/12/7191.3SomePropertiesoffluids1.viscosity(粘性)*Definition：Whenafluidissheared（剪切）,itbeginstomove.Subsequently,apairofforcesappearontheshearsurface,whichresiststheshearmotionofthefluid.Thisiscalled

viscosityThisresistantforceis

shearstress.(剪切应力,内摩擦应力)Infact,thisshearmotionofafluidisakindofdeformation（变形）*Thenatureofviscosity：Forliquidiscohesion（结合）(movie)Forgasisthetransportofmomentum（动量输运）(movie)2023/12/720m:Coefficientofviscosity(粘性系数)[FT/L2]n=m/r:Kinematicviscosity(运动学粘性系数)[L2/T]Velocitygradient*Newtonianlawofviscosity(牛顿粘性定律，牛顿内摩擦定律)UUu(y)xyShearstressThelinearfluid,whichfollowNewtonianresistancelaw,iscalledNewtonianflow.（牛顿流动、牛顿流体）Thevelocitygradientisinfactakindofdeformation.Realfluid(Viscous),Idealfluid(Inviscid&Frictionless)2023/12/7212.Compressibility(压缩性)pressible(不可压):r=constMostliquidflowsaretreatedaspressible.Only1percentincreaseifpressureincreaseby220Compressible（可压缩）:r=r(P.T)Gasescanalsobetreatedaspressiblewhentheirvelocityislessthan0.3Manumbers3.StateRelationsforGasesPerfect-gasLaw（理想气体状态方程）2023/12/7224.ThermalConductivity(热传导)

:

heatfluxinndirectionperunitareak:coefficientofthermalconductivityT:temperaturen:directionofheattransferFourier’slawofheatconduction2023/12/7231.4Twodifferentpointsofviewinanalyzingproblemsinmechanics*TheEulerianview(欧拉观点)andtheLagrangianview（拉格朗日观点）TheEulerianviewisconcernedwiththefieldofflow,appropriatetofluidmechanics.TheLagrangian

viewfollowsanindividualparticlemovingthoughtheflow,appropriatetosolidmechanics.Thecontrastoftwoframes2023/12/724*Flowclassification(流动分类)AccordingtoEulerianview,anypropertyisfunctionofcoordinates（space）andtime.InCartesiansystem(直角坐标系)，itcanbeexpressedasf(x,y,z,t)x,y,z,t:Eulerianvariablecomponent(欧拉变数)f:Functionofonlyonecoordinatecomponent,one-dimensional

(一维

1-D）.Inthelikemanner,two-dimensional（二维2-D）

,three-dimensional

(三维

3-D)

:Functionoftime~~unsteady

(非定常)Otherwisesteady(定常)2023/12/725OneTwodimensionalThreeSteadyUnsteadyCompressiblepressibleViscousInviscid2023/12/7261.5Streamline(流线),Pathline(迹线)&Flowfield(流场)*Whatisastreamline

Astreamlineisthelineeverywheretangenttothevelocityvectoratagiveninstant.2023/12/727

A

pathlineistheactualpathtraversedbyagivenfluidparticles.Forsteadyflow:Streamline=Pathline*WhatisapathlinePathlinesinsteadyflowPathlinesinunsteadyflow2023/12/728FlowPattern(流型、流普、流线族）Streamsurface(流面)&Streamtube(流管）Flowpattern:asetofstreamlinesStreamsurface:acollectionofallthestreamlinespassingthroughalinewhichisnotastreamline.Streamlinecannotintersect（相交），exceptforsingularitypoint(奇点)Streamtube:aclosedcollectionofstreamlines.Noflowacrossstreamtubewalls2023/12/729Flowfield(流场)

：Inagivenflowsituation,thepropertiesofthefluidarefunctionsofpositionandtime,namelyspace-timedistributionsofthefluidproperties.2023/12/730Streamlineequation(流线方程)ds->Infinitesimal(无穷小)dydxds2023/12/731Example:Giventhesteadytwo-dimensionalvelocitydistributionu=kx,v=-ky,w=0,wherekisapositiveconstant.Computeandplotthestreamlinesoftheflow,includingdirection.Solution:

Sincetime(t)doesnotappearexplicitly,themotionissteady,sothatstreamlines,pathlineswillcoincide.Sincew=0,themotionistwo-dimensional.Integrating:Hyperbolas(双曲线)2023/12/732Direction:

u=kx,v=-ky

Quadran